The RCO (Rossby Centre Ocean) model is a Bryan–Cox–Semtner primitive equation circulation model with a free surface (Killworth et al., 1991). Its open boundary conditions are implemented in northern Kattegat, based on prescribed sea level elevation at the lateral boundary (Stevens, 1990). An Orlanski radiation condition (Orlanski, 1976) is used to address the case of outflow, and the temperature and salinity variables are nudged toward climatologically annual mean profiles to deal with inflows (Meier et al., 2003). A Hibler-type dynamic–thermodynamic sea ice model (Hibler, 1979) with elastic–viscous–plastic rheology (Hunke and Dukowicz, 1997) and a two-equation turbulence closure scheme of the k–ε type with flux boundary conditions (Meier, 2001) are embedded into RCO. The deep-water mixing is assumed inversely proportional to the Brunt–Väisälä frequency, with the proportionality factor based on dissipation measurements in the Eastern Gotland Basin (Lass et al., 2003). RCO was used with a horizontal resolution of 2 nmi (3.7 km) and 83 vertical levels, with a layer thickness of 3 m. RCO allows direct communication between bottom boxes of the step-like topography (Beckmann and Döscher, 1997). A flux-corrected, monotonicity-preserving transport (FCT) scheme is applied in RCO (Gerdes et al., 1991). RCO has no explicit horizontal diffusion. For further details of the model setup, the reader is referred to Meier et al. (2003) and Meier (2007).

The model performance of temperature and salinity was evaluated in Meier et al. (2018) and conformed well to observations but showed a higher position of the halocline and slightly lower bottom water salinity, and some deviations with higher temperatures were found in the upper part of the halocline.

The biogeochemical model SCOBI (Swedish Coastal and Ocean Biogeochemical model) has been developed to study the nutrient cycling in the Baltic Sea (Marmefelt et al., 1999; Eilola et al., 2009; Almroth-Rosell et al., 2011, 2015). SCOBI handles biological and ecological processes in the sea as well as sediment nutrient dynamics and is coupled to RCO in this study (e.g., Eilola et al., 2012, 2013, 2014). Resuspension of organic matter is calculated, with the help of a simplified wave model, from the wave and current-induced shear stresses (Almroth-Rosell et al., 2011). The model includes three different functional types representing diatoms, flagellates and other microalgae, and cyanobacteria as well as one zooplankton. SCOBI has a constant carbon-to-chlorophyll a ratio, 50 mg C (mg chl)-1, and the production of phytoplankton assimilates carbon, nitrogen, and phosphorus according to the Redfield molar ratio (106 : 16 : 1, respectively) (Eilola et al., 2009). The molar ratio of complete oxidation of the remineralized nutrients is O2 : carbon = 138. Nitrogen fixation is a function of temperature, light availability, nitrogen-to-phosphorus ratio, and phosphorus concentration in the ambient water (Eilola et al., 2009). Dead organic material, represented by separate variables for nitrogen and phosphorus, accumulates in detritus in the water column and in the sediments. For further details of the “standard” SCOBI model, the reader is referred to Eilola et al. (2009, 2011) and Almroth-Rosell et al. (2011).

In the original SCOBI model, cyanobacteria are represented by one state variable, and the population is upheld by a minimum biomass. The growth is dependent on light, temperature, and nutrients (nitrogen and phosphorus), and nitrogen fixation occurs when the DIN concentration is low after the spring bloom.

The CLC model is seasonal, with only one full life cycle each year (Fig. 3), and simulates four state variables instead of one in the original SCOBI model. It is modified from the detailed life cycle model by Hense and Beckmann (2006) that includes internal nitrogen and energy quotas and the simplified version by Hense and Beckmann (2010). Similar to Hense and Beckmann (2010), growth and life cycle transitions in our CLC model depend only on external factors, but we kept the sinking and rising stages separated, generating an additional life cycle variable. The CLC model equations as well as variables and parameters can be found in Tables S1–S4 in the Supplement.

We distinguish between three life cycle stages (Fig. 3): the growing and nitrogen-fixing stage (vegetative cells with heterocysts, HET), the resting stage (akinetes, AKI), and a stage (REC) where we combine the recruiting (cells with gas vesicles) and the growing non-nitrogen-fixing stage (vegetative cells without heterocysts). REC and HET are assumed to acquire carbon, nitrogen and phosphorus and produce detritus, according to Redfield molar ratios. HETs are positively buoyant, AKIs in the water (AKIW) are sinking and may end up in the sediment (AKIB), and RECs are rising. Dead HETs and RECs end up in the pool of dead organic matter (Fig. 2). Occasions with resuspension may transfer akinetes from the sediment (AKIB) to the water (AKIW).

Life cycle transitions were treated in a relatively simple way: following Hense and Beckmann (2010), we used the in situ growth rate for the transition between the life cycle stages HET and AKI. In autumn, when the growth rate, which is dependent on temperature and light, was below a critical threshold, a transfer into the AKI compartment took place (Eq. 11, Table S3).

For the transition between AKI (AKIB and AKIW) and REC, we prescribed a fixed germination window instead of using a dynamic germination window as proposed by Hense and Beckmann (2010). Between 20 April and the end of April, germination occurred at a constant rate times the AKI concentration (see Eq. 30 in Table S3). This is because the computational costs of a dynamic window in a 3D framework are too high. However, shifting the germination window has only a small impact on the timing of maximum cyanobacteria abundance in summer and the magnitude of nitrogen fixation. A sensitivity test showed that the decadal mean nitrogen fixation was lower when germination was earlier by about 4 %–7 %, while the maximum annual difference found for the entire period (1850–2008) was 14 % lower.

The transition from the recruiting and vegetative state (REC) to the diazotrophic state (HET) takes place when the growth of HET is larger than that of REC (Eq. 10 in Table S3). The maximum growth rate (s-1) of REC is larger than that of HET, but the growth (mmol m-3 s-1) is in the previous state, also dependent on DIN. When DIN is low after the spring bloom, the growth of HET becomes larger than that of REC, and a transition to HET occurs.

The temperature dependence of HET and REC growth is given by the temperature limitation function (Supplement, Table S3, Eqs. S8 and S26). Between approximately 6 and 28 ∘C an increase in temperature positively affects the growth rate of HET and REC while an increase above 28 ∘C instead generates a decline in growth rate. The model equation was designed to represent the observational data presented in Lehtimäki et al. (1997). The original formulation in Hense and Beckmann (2006), based on the same data, was found to be numerically unstable in the 3D model framework and was therefore redesigned. The resulting model formulation closely resembles that of Hense and Beckmann (2006) but gives slightly higher growth rates at low temperatures.

For potential growth of REC and HET and potential transition of AKI to REC, we assumed a salinity span between 3 and 10 PSU, which is in fair agreement with the optimum growth of N. spumigena (5–10 PSU), Aphanizomenon sp. (0–7 PSU) (Rakko and Seppälä, 2014), and Dolichospermum spp. (0–6 PSU) (Teikari et al., 2019). This constrains the cyanobacteria to areas within the Baltic Sea that lie within the given salinity span. The AKIB is assumed to be rapidly immobilized in the sediment, simulated as a very large burial, under salinity outside of the defined range.

Similar to Hense and Beckmann (2006, 2010), we pooled the three main important nitrogen-fixing taxa N. spumigena, Aphanizomenon sp., and Dolichospermum spp. into one functional cyanobacteria group. We are well aware that there are differences among the species (e.g., with respect to salinity and/or temperature dependence), and thus we may not expect to be able to reproduce specific local patterns, for example in a low-salinity region outside of the range where some of the taxa can still thrive. Nevertheless, as we will show, our model was able to reproduce the main seasonal and spatial patterns of biomass and nitrogen fixation.

We herein refer to the 3D coupled RCO–SCOBI that includes the new CLC as SCOBI-CLC while the old model version without CLC will be referred to as SCOBI.

The historical simulation uses reconstructed atmospheric, hydrological, and nutrient load forcing and daily sea levels at the lateral boundary for the period 1850–2008 as described in detail in Meier et al. (2018) and Gustafsson et al. (2012) and references therein. The used high-resolution atmospheric forcing fields for the period 1850–2008 were reconstructed using atmospheric model data for 1958–2007 together with historical station data of daily sea-level pressure and monthly air temperature observations. For the calculation of monthly mean river flows, five different historical datasets were merged. The basin-integrated reconstructed nutrient loads from land and atmosphere to the present model are the same as used and described by Gustafsson et al. (2012). Nutrient loads contain both organic and inorganic phosphorus and nitrogen. In the present SCOBI version, the nitrogen and phosphorus detritus was separated and thus used both organic phosphorus and nitrogen from the forcing. This is the only difference in forcing from the present SCOBI model compared to the model used by Meier et al. (2018), where detritus consisted of one pool limited by the Redfield ratio. Daily mean sea level elevations at the boundary in the northern Kattegat were calculated from the reconstructed, meridional sea level pressure gradient across the North Sea. In case of inflow, temperature, salinity, nutrients, and detritus values were nudged towards observed climatological seasonal mean profiles for 1980–2005 at the monitoring station Å17 in the southern Skagerrak. Nutrient concentrations before 1900 were assumed to be only 85 % of present-day concentrations. A linear decrease in nutrient concentrations from 1950 and back in time to 1900 was assumed.

The Swedish National Marine Monitoring Program includes monthly tube sampling of phytoplankton abundance (including filamentous cyanobacteria) and water collection for chemical and physical parameters (e.g., inorganic nutrients, oxygen, salinity, temperature). These data are hosted by the Swedish National Oceanographic Data Centre at the Swedish Hydrological and Meteorological Institute and are freely accessible at https://www.smhi.se (last access: March 2019). For this work, we also used data of oxygen and nutrients from the Baltic Environmental Database (BED), which include post-processed monitoring station data from a number of institutes around the Baltic Sea. The data are freely available at http://nest.su.se/bed (last access: January 2017). The cyanobacteria biovolume (mm3 L-1) was calculated based on cell numbers and size of filaments (Olenina et al., 2006) and further to carbon concentrations (referred to as cyanobacteria biomass) based on Menden-Deuer and Lessard (2000). Concentrations of inorganic nutrients and oxygen were extracted from the database for station BY15 in the Eastern Gotland Basin and cyanobacteria biomass for four stations in the Baltic Proper for 1999–2008 (Fig. 1).

The cyanobacteria biovolume was used to estimate nitrogen fixation rates (mmol N m-2 d-1) based on empirical biovolume-specific measurements (Klawonn et al., 2016) according to calculations in Olofsson et al. (2021). Shortly, the observed biovolumes (mm3 L-1) were multiplied with biovolume-specific measurements (µmol N mm-3 d-1) and further integrated over 0–10 m to obtain area-specific nitrogen fixation rates (mmol N m-2 d-1). These rates were summarized, first monthly and then for the whole year, and multiplied with the size of the Baltic Proper (200 000 km2) to provide annual nitrogen loads via nitrogen fixation by filamentous cyanobacteria (kt N yr-1) in 1999–2008.

In the original model by Hense and Beckmann (2006) that includes the internal energy and nitrogen, the seasonal changes in cyanobacteria biomass are adequately modeled without taking phosphate into account. The rapid decrease in HET in autumn is then a result of an internal energy crisis caused by the high energy demand of nitrogen fixation together with decreasing temperatures and light. This is also true for the simplified model of Hense and Beckmann (2010) where the growth rate of HET is strongly limited by temperature. However, in the Baltic Sea, the phosphorus concentrations may limit the cyanobacteria biomass (Klawonn et al., 2016; Degerholm et al., 2006; Olofsson et al., 2016). We have therefore performed four sensitivity runs, listed below, to evaluate the role of phosphorus uptake. We distinguish between uptake of inorganic and organic phosphorus, since both types are utilized by cyanobacteria (Schoffelen et al., 2018). The preferential uptake of dissolved inorganic phosphorus is, however, assumed in the model.  

noP – Phosphorus is excluded from cyanobacteria in line with Hense and Beckmann (2010). In this case, the cyanobacteria can grow completely independently of phosphate availability in ambient water. The cyanobacteria also do not, in this case only, take up or release any phosphate.

To estimate cyanobacteria biomass and nitrogen fixation rates and compare with observations for the Baltic Proper, we used the phosphorus limitation setting wPlim based on the limitation experiments that best captured the size of biomass and the seasonal timing (Fig. 4). Compared to the SCOBI, SCOBI-CLC displays significant improvements in seasonal timing (Fig. 8). In line with observations, SCOBI-CLC generates a peak biomass in July, while the SCOBI results reach peak biomass in September. This is an important improvement attained by using the CLC model compared to previous results (Hieronymus et al., 2018) as the seasonal timing of biomass affects also the timing and size of nitrogen fixation. By obtaining a bloom more constrained to the summer months, a larger nitrogen fixation due to higher temperatures was observed using SCOBI-CLC. The updated nitrogen fixation rates were also in the same range as estimates based on measurements for the same stations during the years 1999–2008, both in magnitude and timing (Fig. 9).

For nitrogen fixation, there was a slight difference where SCOBI-CLC displayed a prolonged peak period in July–August while the observations showed a peak more constrained to July. The strong coherence between modeled and observed nitrogen fixation is somewhat surprising given the larger cyanobacteria biomass in SCOBI-CLC compared to observations (Fig. 8). There may be several reasons for this discrepancy. The frequency of observations is bimonthly at most, which occasionally means missed peak values. Furthermore, the cyanobacteria biovolume from observations was used with different presumptions to estimate the nitrogen fixation rates and to calculate carbon concentrations. The modeled nitrogen fixation is calculated during the run from the growth of HET in the CLC model while the carbon content of cyanobacteria is calculated by the Redfield ratio between nitrogen and carbon in HET with a minor contribution also from REC. Hence, there are uncertainties in the calculations of carbon biomass from both observations and from model results. It is not easy to change the Redfield C : N : P ratio that is used in the model since the results from the entire biogeochemical cycle including the oxygen consumption in the model are dependent on this ratio. There are other biogeochemical models with variable C : N : P ratios that might be used to analyze the impact from these processes further (e.g., Fransner et al., 2018; Kwiatkowski et al., 2018). Uncertainties in the comparison of models and observations also stem from the fact that observations are done on small water samples from an area that is covered by an average value from a 3.7 km × 3.7 km grid in the model.

Nitrogen fixation in the Baltic Sea is dominated by the three filamentous taxa described herein (Klawonn et al., 2016). However, heterotrophic nitrogen fixation has also been observed in the Baltic Sea (e.g., Farnelid et al., 2013), but since their rates are extremely low in this region, they do not affect the overall input of nitrogen (heterotrophic bacteria: up to 0.44 nmol L-1 d-1 in Farnelid et al., 2013, as compared to 800 nmol L-1 d-1 by the filamentous cyanobacteria in Klawonn et al., 2016).

We estimated the internal nitrogen load via nitrogen fixation to the Baltic Proper based on monitoring and in situ measurements to a mean of 399 kt yr-1 for 1999–2008, but with a large variation among years (SD ± 104). This is slightly below the external load from river runoff and atmospheric deposition of 430 kt yr-1 (±54), provided by HELCOM (2018). For SCOBI-CLC, we got an estimated mean nitrogen load of 409 kt yr-1 for the experiment wPlim over the same years for the Baltic Proper (calculated over an area of 216 600 km2) compared to 271 kt yr-1 for SCOBI. The estimated annual nitrogen load via nitrogen fixation to the Baltic Proper has not changed over recent years (2013–2017 in Olofsson et al., 2021) and is in the range of other studies for the Baltic Proper (310 kt in Rolff et al., 2007; 370 kt in Wasmund et al., 2001; 396 kt in Svedén et al., 2016) but below the estimated load of 613 kt in Wasmund et al. (2005), 514 kt in Gustafsson et al. (2013), and 511 kt in Schneider et al. (2009).

The mean vertical profiles of phosphate, DIN, and oxygen at stations BY5 and BY15 showed an overall good representation by both SCOBI-CLC and SCOBI (Fig. 10). Below the mixed layer, the DIN concentrations were high compared to observations for SCOBI-CLC, and the deep water phosphate at BY5 was a bit too low. Surface phosphate is slightly closer to observations for SCOBI-CLC than for SCOBI. The low surface DIN in both model versions is a reflection of low nitrate concentrations compared to observations which were also reported by Meier et al. (2012) and Saraiva et al. (2018). The low surface DIN is also demonstrated in Fig. 7 where the noP experiment gave rise to higher DIN concentrations as nitrogen fixation due to strong cyanobacteria blooms, in this case, adds more DIN to the water column. Despite the shortcomings, the trends for both nutrients and oxygen were well captured by both SCOBI-CLC and SCOBI.